2cos^3(x)+cos^2(x)-2cos(x)-1=0

Solución

2 cos^{3} (x) + cos^{2} (x) - 2 cos (x) - 1 = 0

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = π + 2 πn, x = 2 πn

Pasos de solución

2 cos^{3} (x) + cos^{2} (x) - 2 cos (x) - 1 = 0

Usando el método de sustitución

cos (x) = - \frac{1}{2}, cos (x) = - 1, cos (x) = 1

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combinar toda las soluciones

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = π + 2 πn, x = 2 πn

3 tan (θ + 4 3^{\circ}) = 2 cos (θ + 4 3^{\circ})

2 sin (θ) cos (θ) + 2 cos (θ) = 0

3 tan (2 x) = 5

3 - 2 cos (θ) = 3 - 2 sin (θ)

(4 cos (x) - 2 sin (x))^{2} + 12 sin^{2} (x) = 16